A multi-objective cutting parameter optimization method
By combining the Harris Eagle optimization algorithm with a BP neural network and the response surface methodology and entropy weight method, a multi-objective cutting parameter optimization model is constructed. This model solves the problems of insufficient model accuracy and decision objectivity in metal cutting parameter optimization, and achieves synergistic optimization of energy consumption and surface quality. It is applicable to various workpiece materials and processing conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2026-05-26
- Publication Date
- 2026-06-26
Smart Images
Figure CN122284508A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cutting parameter optimization technology, and specifically relates to a multi-objective cutting parameter optimization method. Background Technology
[0002] Metal cutting, as a fundamental process in manufacturing, directly impacts processing efficiency, workpiece quality, and production costs through the selection of its process parameters. In the context of sustainable development in manufacturing, environmental indicators such as energy consumption and carbon emissions are increasingly becoming crucial considerations for optimizing cutting parameters. This has driven the optimization problem to evolve from a traditional single-objective model to a multi-objective collaborative optimization approach that encompasses factors such as energy consumption and surface integrity.
[0003] Traditional process parameter optimization methods are mostly based on empirical formulas or simplified mechanistic models. The former has limited applicability under different processing conditions, while the latter struggles to accurately characterize the inherent laws of strongly nonlinear processes, resulting in poor prediction accuracy. To address this issue, some studies have attempted to introduce neural network algorithms to establish a nonlinear mapping relationship between process parameters and optimization objectives. However, conventional neural network models generally suffer from drawbacks such as slow convergence speed and susceptibility to local extrema.
[0004] Furthermore, in current multi-objective optimization research, most methods only adopt a single modeling strategy, making it difficult to differentiate modeling based on the characteristics of each optimization objective. In the final decision-making stage, the non-dominated solution set obtained from multi-objective optimization often relies on human experience for screening, lacking a systematic and objective evaluation mechanism.
[0005] Therefore, there is an urgent need for a cutting parameter optimization scheme that integrates high-precision modeling and intelligent multi-objective optimization decision-making to overcome the shortcomings of existing technologies in terms of model accuracy, multi-objective collaborative optimization capability, and decision objectivity. This would enable collaborative optimization of surface quality and energy consumption control, and meet the actual needs for comprehensive optimization of process parameters in the context of sustainable manufacturing. Summary of the Invention
[0006] To overcome the problems in the prior art, this invention proposes a multi-objective cutting parameter optimization method.
[0007] The technical solution of the present invention to solve the above-mentioned technical problems is as follows: This invention provides a method for optimizing multi-objective cutting parameters, comprising the following steps: Step 100: Collect the cutting parameters of the selected workpiece material and the machine tool spindle power signal during the cutting process, calculate the cutting specific energy, and collect the surface roughness of the workpiece surface at the same time; Step 200: Construct a BP neural network model, optimize the weights and thresholds of the BP neural network using the Harris Eagle optimization algorithm, and establish a cutting energy prediction model with cutting parameters as input and cutting energy as output, taking the minimization of the fitness function as the optimization objective. Step 300: Construct a surface roughness prediction model with the coded variables of cutting parameters as input and surface roughness as output; Step 400: Based on the cutting specific energy prediction model and the surface roughness prediction model, establish a multi-objective cutting parameter optimization model; Step 500: Solve the multi-objective cutting parameter optimization model to obtain the Pareto non-dominated solution set; Step 600: After obtaining the Pareto non-dominated solution set, the entropy weight method is used for comprehensive decision-making, and the solution with the largest comprehensive evaluation value is selected as the optimal cutting parameter combination.
[0008] Furthermore, in step 100, the cutting parameters include the extreme values of rotational speed, feed per tooth, axial depth of cut, and radial depth of cut.
[0009] Further, in step 100, the cutting parameters of the selected workpiece material and the machine tool spindle power signal during the cutting process are collected, and the cutting specific energy is calculated, including: Calculate the material removal rate of the workpiece based on the cutting parameters of the selected workpiece material; Based on the machine tool spindle power signal, the total energy consumed during the machining process is calculated by integration. The cutting specific energy is calculated based on the workpiece material removal rate and the total energy consumed during the processing.
[0010] Furthermore, step 100 also includes: The collected cutting parameters and cutting specific energy were matched, and the collected cutting parameters and surface roughness were matched to construct an experimental dataset. The experimental dataset was preprocessed by normalization; and the preprocessed experimental data was divided into training set and test set.
[0011] Further, step 200 includes: Construct a BP neural network model, setting the input layer as cutting parameters and the output layer as cutting specific energy; Encode all connection weights and thresholds in the BP neural network model into position vectors of individuals in the Harris Eagle optimization algorithm, and define a fitness function; The connection weights and thresholds of the BP neural network model are optimized using the Harris Eagle optimization algorithm to minimize the fitness function, thus establishing an objective function for the nonlinear mapping between cutting parameters and cutting specific energy.
[0012] Furthermore, the fitness function is the sum of the mean squared error of the BP neural network model on the training set and the mean squared error on the test set.
[0013] Further, step 300 includes: Convert cutting parameters into encoded variables; Based on the coded variables of cutting parameters, a quadratic polynomial model is established using the response surface methodology to represent the relationship between the coded variables of cutting parameters and the predicted values of surface roughness, i.e., the surface roughness prediction model.
[0014] Furthermore, in step 400, when establishing the multi-objective cutting parameter optimization model, it is also necessary to set constraints on the cutting parameters.
[0015] Furthermore, in step 500, the multi-objective cutting parameter optimization model is solved using a decomposition-evolutionary algorithm to obtain a Pareto non-dominated solution set.
[0016] Further, step 600 includes: Based on the Pareto non-dominated solution set, each solution is dimensionless. Calculate the information entropy, and use the information entropy to calculate the weight of each objective function; The comprehensive evaluation value is calculated based on the solutions under each objective function after dimensionless processing and the weight of each objective function. Compare the comprehensive evaluation values of all solutions, and select the solution with the largest comprehensive evaluation value as the optimal combination of cutting parameters.
[0017] Compared with the prior art, the present invention has the following technical effects: (1) High modeling accuracy: This invention targets the highly nonlinear target of processing energy consumption, and uses the Harris Eagle optimization algorithm to improve the BP neural network for modeling. By utilizing the characteristics of the HHO algorithm, which has strong global search capability and fast convergence speed, it effectively solves the problem that traditional BP neural networks are prone to getting trapped in local optima, and significantly improves the accuracy and stability of the energy consumption prediction model.
[0018] (2) Differentiated modeling strategy: This invention adopts differentiated modeling methods for different optimization objectives. For energy consumption, an HHO-BP neural network is used, and for surface roughness, a response surface methodology is used. This hybrid modeling strategy fully considers the physical characteristics of each objective, making the model accuracy better than that of a single modeling method.
[0019] (3) Uniform distribution of solution set: The present invention adopts a multi-objective evolutionary algorithm based on decomposition for multi-objective optimization. By decomposing the multi-objective problem into multiple single-objective sub-problems through weight vectors, a uniformly distributed Pareto non-dominated solution set can be obtained, providing decision-makers with a variety of alternative solutions.
[0020] (4) Strong objectivity of decision making: This invention introduces the entropy weight method to make objective decisions on the Pareto non-dominated solution set. It calculates the weight of each index based on the dispersion of the data itself, avoiding the bias caused by subjective weighting, and making the selection of the optimal process parameters more scientific and objective.
[0021] (5) Wide range of applications: The method of the present invention has good generalization ability and adaptability. It can be applied to the cutting parameter optimization problem of different workpiece materials, different tool combinations and different processing conditions by only adjusting the experimental data and model parameters. Attached Figure Description
[0022] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 This is a flowchart of the HHO-BP algorithm of the present invention; Figure 2 This is a diagram showing the prediction results of the HHO-BP model of the present invention; Figure 3 This is a flowchart of the present invention; Figure 4 The attached figure shows the experimental diagram of the entropy weight method of this invention. Detailed Implementation
[0024] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.
[0025] This invention provides a multi-objective optimization method aimed at intelligently optimizing process parameters in metal cutting. It integrates a BP neural network improved from the Harris Eagle optimization algorithm, response surface methodology, a decomposition-based multi-objective evolutionary algorithm, and entropy weighting method to construct a complete technical chain of "high-precision modeling - intelligent optimization - objective decision-making," thereby reducing machining energy consumption, improving surface roughness, and enhancing overall machining performance.
[0026] In this embodiment, refer to Figures 1-4A multi-objective cutting parameter optimization method is provided, including the following steps: Step 100: Collect the cutting parameters of the selected workpiece material and the machine tool spindle power signal during the cutting process, calculate the cutting specific energy, and collect the surface roughness of the workpiece surface at the same time; Step 200: Construct a BP neural network model; use the Harris Eagle optimization algorithm to optimize the weights and thresholds of the BP neural network, and take minimizing the fitness function as the optimization objective to establish a cutting energy prediction model with cutting parameters as input and cutting energy as output; Step 300: Construct a surface roughness prediction model with the coded variables of cutting parameters as input and surface roughness as output; Step 400: Based on the cutting specific energy prediction model and the surface roughness prediction model, establish a multi-objective cutting parameter optimization model; Step 500: Solve the multi-objective cutting parameter optimization model to obtain the Pareto non-dominated solution set; Step 600: After obtaining the Pareto non-dominated solution set, the entropy weight method is used for comprehensive decision-making, and the solution with the largest comprehensive evaluation value is selected as the optimal cutting parameter combination.
[0027] The following is a detailed explanation of each of the above steps: Step 100: Collect the cutting parameters of the selected workpiece material and the machine tool spindle power signal during the cutting process, and calculate the cutting specific energy; at the same time, collect the surface roughness of the workpiece surface.
[0028] As an example, step 100 specifically includes: Step 110: Obtain the cutting parameters for the selected workpiece material.
[0029] Obtain the cutting parameters of the selected workpiece material, including the extreme values of rotational speed, feed per tooth, axial depth of cut, and radial depth of cut.
[0030] Based on the extreme values of the cutting parameters, three level values are determined for each cutting parameter. For example, for the rotational speed, low, medium, and high speed values can be determined according to the machine tool performance and workpiece material characteristics; a similar method is used to determine the three level values for feed per tooth, axial depth of cut, and radial depth of cut.
[0031] Based on the determined four factors (rotation speed, feed per tooth, axial depth of cut, and radial depth of cut) and three levels, orthogonal arrays, such as the L27 orthogonal array, are selected to create an orthogonal experimental table. This orthogonal experimental table makes full use of the uniform dispersion and neat comparability of orthogonal arrays, and significantly reduces the number of experiments while ensuring the representativeness of the experiments, thereby reducing experimental costs and time costs.
[0032] Cutting experiments were conducted on the machine tool according to the experimental plan arranged in the orthogonal experimental table. Each experiment was repeated three times to reduce random errors during the experiment and improve the reliability of the experimental data. During each experiment, the cutting parameters were strictly controlled according to the experimental plan to ensure the consistency of the experimental conditions.
[0033] Step 120: Calculate the material removal rate of the workpiece based on the cutting parameters of the selected workpiece material; collect the machine tool spindle power signal during the cutting process, obtain the total energy consumed in the machining process through integration calculation, and calculate the cutting specific energy based on the material removal rate of the workpiece.
[0034] Calculate the material removal rate based on the cutting parameters of the selected workpiece material. : ; In the above formula, Indicates the number of teeth on the cutting tool; The material removal rate of the workpiece removed during milling is expressed in mm³ / s (cubic millimeters per second); n is the machine tool spindle speed, expressed in r / min (revolutions per minute). Indicates radial depth of cut, in mm (millimeters); Indicates the axial depth of cut, in mm; This indicates the feed per tooth, expressed in mm / z (millimeters per tooth).
[0035] The machine tool spindle power signal during the cutting process is collected, and the total energy consumed during machining is calculated through integration. Based on the workpiece material removal rate, the cutting specific energy is calculated. The cutting specific energy is defined as the energy consumed per unit volume of material removed, and its expression is: ; In the above formula, This indicates the material removal rate of the workpiece, expressed in mm³ / s. t Indicates the cutting time; This represents the cutting specific energy, expressed in J / mm. 3 (Joules per cubic millimeter); This represents the total energy consumption during the cutting process, expressed in J (joules).
[0036] Step 130: Simultaneously, the surface roughness of the workpiece surface is collected using a three-dimensional optical profile measuring instrument. An experimental dataset is constructed based on the cutting parameters and cutting specific energy, and then preprocessed.
[0037] The collected cutting parameters and specific energy data are organized and matched. Each set of experiments corresponds to a data sample based on the corresponding cutting parameters and specific energy. All samples are combined to form the experimental dataset. For example, in one set of experiments, the rotational speed is... 1. Feed per tooth is 1. Axial depth of cut is 1. Radial depth of cut is 1. The calculated cutting specific energy is: 1. This constitutes a sample in the dataset. The 3D optical profile measurement instrument used is a VK-X260 laser confocal microscope.
[0038] Simultaneously, the collected cutting parameters and surface roughness are organized and matched. The cutting parameters and surface roughness corresponding to each set of experiments constitute a data sample, and all samples are combined to form an experimental dataset.
[0039] The experimental dataset is preprocessed by normalization, normalizing all data to the interval [0,1]. The corresponding formula can be written as: ; In the above formula, This refers to the raw data, i.e., the original values of cutting parameters, cutting specific energy, etc., collected or calculated from the experimental dataset; This represents the normalized data; This represents the minimum value of the variable in the sample. This represents the maximum value of the variable in the sample, that is, the maximum value of the variable among all samples.
[0040] This normalization process eliminates differences in units and orders of magnitude between different variables, making the data comparable and facilitating subsequent data analysis and model building.
[0041] The preprocessed experimental data were divided into training and test sets. The prediction model was trained using the training set data, and the model parameters were adjusted so that the model could fit the relationship between cutting parameters and cutting specific energy better. The trained model was validated using the test set data to evaluate the model's prediction accuracy and generalization ability.
[0042] Step 200: Construct a BP neural network model; use the Harris Eagle optimization algorithm to optimize the weights and thresholds of the BP neural network, and take the minimization of the fitness function as the optimization objective to establish a cutting energy prediction model with cutting parameters as input and cutting energy as output.
[0043] As an example, step 200 specifically includes: Step 210: Construct the BP neural network model.
[0044] Construct a BP neural network model, setting the input layer nodes as cutting parameters, including rotational speed. Feed per tooth Axial depth of cut and radial depth The output layer nodes are set to cutting specific energy (SEC), and the number of hidden layer nodes is determined. The selection range of hidden layer nodes is often determined using empirical formulas. ; In the formula, This represents the number of neurons in the hidden layer. p represents the number of neurons in the input layer; p represents the number of neurons in the output layer. 1 Integers within the range of 13. Based on the formula, the number of hidden layer nodes in the neural network is selected within the range of 4-15. The BP neural network training model is performed three times at each hidden layer node, and the mean absolute percentage error (MASE) of each node is recorded. The node with the smallest MSE is selected as the number of hidden layer nodes. Preferably, the optimal number of hidden layer neurons is 6-9.
[0045] The choice of the number of hidden layer nodes affects the model's performance; too many may lead to overfitting, while too few may lead to underfitting. Connection weights are parameters of the strength of connections between neurons, while thresholds are parameters of the activation threshold of neurons. Connection weights and thresholds together determine the mapping relationship of the neural network.
[0046] Step 220: Encode all connection weights and thresholds in the BP neural network model into position vectors of individuals in the Harris Eagle optimization algorithm, and define the fitness function.
[0047] All connection weights and thresholds in the BP neural network model are encoded as position vectors for individuals in the Harris Eagle Optimization (HHO) algorithm. This encoding method enables the HHO algorithm to optimize the parameters of the neural network.
[0048] Encode all connection weights and thresholds in the BP neural network model into position vectors for individuals in the Harris Eagle Optimization (HHO) algorithm, specifically including: Initialize HHO algorithm parameters: Initialize parameters such as population size, maximum number of iterations, and search boundary. Population size determines the number of individuals in the HHO algorithm; a larger population size can increase search diversity but also increases computational cost. The maximum number of iterations limits the search process to prevent infinite loops. The search boundary limits the range of values for individual position vectors, ensuring that the parameters are within a reasonable range.
[0049] Define the fitness function: Each individual is decoded into a set of initial weights and thresholds for a backpropagation (BP) neural network, and the sum of the mean squared errors of the BP neural network on the training and test sets is used as the fitness function. Specifically, the fitness function is as follows: ; In the above formula, Represents the fitness function; This represents the mean squared error of the training set; This represents the mean square error of the test set.
[0050] ; ; In the above formula, Represents the mean square error function; This represents the constructed BP neural network model; This represents the set of true cutting specific energy values for the training set; This represents the set of predicted cutting energy values obtained by the BP neural network model from the training set data; This represents the set of true cutting specific energy values for the test set; This represents the set of predicted cutting energy values obtained by the BP neural network model based on the test set data.
[0051] The corresponding mathematical form can be written as: ; ; In the above formula, Indicates the number of samples in the training set; Indicates the number of samples in the test set; Indicates the true SEC value; This indicates a predicted SEC value.
[0052] Step 230: Optimize the connection weights and thresholds of the BP neural network using the Harris Eagle optimization algorithm to minimize the fitness function and establish the objective function for the nonlinear mapping between cutting parameters and cutting specific energy.
[0053] The HHO algorithm iteratively updates the individual positions, searching for the optimal combination of weights and thresholds in the search space. In each iteration, the HHO algorithm updates and selects individuals based on their fitness values, gradually approaching the optimal solution. After finding the optimal combination of weights and thresholds, it is used as the initial parameters for training a BP neural network. The training data is used to adjust the weights and perform backpropagation of errors in the neural network, ultimately obtaining a cutting energy specificity prediction model. This model can predict the cutting energy specificity based on the input cutting parameters, thereby assessing the machining energy consumption.
[0054] The cutting energy prediction model takes spindle speed, feed per tooth, radial depth of cut, and axial depth of cut as inputs and cutting energy as output. Its objective function can be expressed as: ; in, The vector of cutting parameters to be optimized.
[0055] Step 300: Construct a surface roughness prediction model with the coded variables of cutting parameters as input and surface roughness as output.
[0056] Convert cutting parameters into encoded variables: ; In the above formula, The encoded variable representing rotational speed; The encoded variable representing the feed per tooth; The coded variable representing the axial cutting depth; The encoded variable represents the radial cutting depth.
[0057] Based on the encoded variables of cutting parameters, a quadratic polynomial model is established using the response surface methodology. Its general form is as follows: ; In the above formula, Y represents the surface roughness; These are the constant coefficients of the model; , It is the first i The and the first j The input variables include the spindle speed, feed per tooth, radial depth of cut, and axial depth of cut in the milling parameters; , , These represent the linear effects, interactions, and secondary effects of the model, respectively.
[0058] Preferably, in the encoded variable , , , The surface roughness prediction model can be expressed as follows: Ra=β 0 +β 1 A+β 2 B+β 3 C+β 4 D+β 12 AB+β 13 AC+β 14 AD+β 23 BC+β 24 BD+β 34 CD+β 11 A2+ β 22 B2+β 33 C2+β44 D2 ; In the above formula, β0 is the predicted surface roughness value; β0 is a constant term that reflects the baseline level of the model. β 1 β 4 is the coefficient of the linear term, representing the degree of linear influence of each factor on surface roughness; β 12 β 34 The interaction coefficients reflect the influence of the interactions between factors on surface roughness; β 11 β 44 The coefficients are quadratic terms, reflecting the nonlinear influence of each factor on surface roughness.
[0059] Multiple regression analysis was performed using statistical software such as Minitab / R, and the collected coded variable data and corresponding surface roughness data were input into the software.
[0060] The coefficients in the model were obtained by regression analysis using the least squares method based on experimental data in Design-Expert software. β The value of R was determined, and a model significance test was performed (p<0.05). R was then adjusted. 2 A value greater than 0.9 is required to ensure the model's goodness of fit to the data, meaning the model can well explain variations in surface roughness. Specifically:
[0061]
[0062] ; In the above formula, This is the predicted value for surface roughness.
[0063] Step 400: Based on the cutting specific energy prediction model and the surface roughness prediction model, establish a multi-objective cutting parameter optimization model.
[0064] As an example, step 400 specifically includes: Step 410: Determine the multi-objective function based on minimizing the cutting specific energy and minimizing the surface roughness.
[0065] Define the two objective functions of the multi-objective cutting parameter optimization model: The first objective is to minimize the cutting specific energy, which is expressed as follows: Cutting specific energy reflects the energy consumed per unit of material removed; reducing cutting specific energy helps improve the energy efficiency of machining.
[0066] The second objective is to minimize the surface roughness, expressed as: Surface roughness is an important indicator for measuring the quality of machined surfaces; lower surface roughness means higher surface quality.
[0067] Combining the two objectives, a multi-objective cutting parameter optimization model is established, and the multi-objective cutting parameter optimization function is: ; In the above formula, This represents minimizing a multi-objective function.
[0068] Step 420: Set the constraints for the cutting parameters.
[0069] Based on the actual machining conditions and equipment capabilities, determine the value range of each cutting parameter: ; These constraints ensure that the combination of cutting parameters generated during the optimization process is feasible and safe in actual machining.
[0070] Step 500: Use the decomposition-evolutionary algorithm to solve the multi-objective cutting parameter optimization model and obtain the Pareto non-dominated solution set.
[0071] The MOEA / D (Multi-Objective Evolutionary Algorithm based on Decomposition) algorithm is preferred. This algorithm decomposes the multi-objective problem into multiple scalar quantum problems, which can effectively handle multi-objective optimization problems and find a set of approximate Pareto optimal solutions.
[0072] For each scalar quantum problem, a sub-objective function is constructed using the Tchebycheff decomposition method, and its expression is as follows: ; In the above formula, This represents the sub-objective function constructed using the Tchebycheff decomposition method; This represents the weight vector, used to balance the importance of each objective function; The representation is an ideal point, a vector composed of the minimum values of each objective function within the feasible region; Indicates the first j One objective function.
[0073] Based on the number and characteristics of the objective function, a set of uniformly distributed weight vectors is constructed. A neighborhood is determined for each weight vector, and the size of the neighborhood is determined by the Euclidean distance between the weight vectors. The scalar quantum problems corresponding to the weight vectors within the neighborhood have similar properties.
[0074] By constructing weight vectors and neighborhood structures, and performing crossover, mutation, and update operations within the neighborhood, the Pareto optimal front is gradually approximated to obtain a non-dominated solution set, specifically including: During the iteration process, for the current subproblem, two individuals with cutting parameters are randomly selected as parents within its neighborhood, and new individuals are generated using simulated binary crossover (SBX) according to the preset crossover probability; Perform polynomial mutation operations on new individuals according to preset mutation probabilities to improve population diversity and global search capabilities; The newly generated individual is input into the multi-objective cutting parameter optimization model to calculate the corresponding cutting specific energy and surface roughness objective function values, and update the current ideal point; the objective function value of the newly generated individual is calculated and compared with the objective function value of the original individual in the neighborhood; if the new individual performs better on a certain scalar quantum problem, the original individual is replaced, and the Pareto optimal front is gradually approached. After multiple iterations, when the algorithm meets the termination conditions, such as reaching the maximum number of iterations or the objective function value converging, a set of Pareto non-dominated solutions is obtained.
[0075] Step 600: After obtaining the Pareto non-dominated solution set, the entropy weight method is used for comprehensive decision-making, and the solution with the largest comprehensive evaluation value is selected as the optimal cutting parameter combination.
[0076] After completing the multi-objective optimization, a set of Pareto non-dominated solutions is obtained. Each solution corresponds to a set of cutting parameters and the corresponding objective function values (cutting specific energy and surface roughness).
[0077] As an example, step 600 specifically includes: Step 610: Based on the Pareto non-dominated solution set, perform dimensionless processing on each solution.
[0078] For indices where smaller values are always better, such as cutting specific energy and surface roughness, a range transformation method is used for dimensionless processing. For each solution value under each objective function, dimensionless processing is applied, mapping the data to the [0, 1] interval to eliminate the influence of different objective function dimensions and orders of magnitude. ; In the above formula, Indicates the first i The solution is at the th solution. j The original values under the objective function i Denotes the first solution in the Pareto solution set. i Group cutting parameter combinations, j When =1, it corresponds to the cutting specific energy SEC. j =2 corresponds to the surface roughness; This represents the value of each solution under each objective function after dimensionless processing.
[0079] Step 620: Calculate information entropy.
[0080] Calculate information entropy: ; K ; In the above formula, m This represents the number of solutions in the Pareto non-dominated solution set; K represents a constant in the calculation of information entropy. Indicates the first i The solution is at the th solution. j The proportion of the dimensionless value under a given objective function to the sum of the dimensionless values of all solutions under that objective function; Indicates the first j The information entropy of an objective function reflects the degree of dispersion of its value.
[0081] Information entropy reflects the degree of dispersion of the objective function value. The greater the dispersion, the smaller the information entropy, and the higher the importance of the objective function in the comprehensive evaluation. Calculate the weights of each objective function using information entropy. : ; Weights represent the relative importance of each objective function in the overall evaluation; the smaller the information entropy of an objective function, the greater its weight usually is.
[0082] Step 630: Based on the solutions under each objective function after dimensionless processing and the weights of each objective function, calculate the comprehensive evaluation value. : ; Compare the overall evaluation values of all solutions The solution with the largest comprehensive evaluation value is selected as the optimal cutting parameter combination. This optimal cutting parameter combination achieves the optimal balance under the comprehensive consideration of the two objectives of cutting specific energy and surface roughness.
[0083] Figure 2 This graph compares the predicted and actual values of the HHO-BP model. The horizontal axis represents the test sample number, and the vertical axis represents the specific energy difference (SEC) value. The blue curve represents the actual experimental value, and the red curve represents the model prediction value. The graph shows that the trends of the model prediction and the actual experimental value are basically consistent, indicating that the established HHO-BP model has good prediction accuracy and generalization ability. (Reference) Figure 4 , Figure 4 The figure below shows the experiment of the entropy weight method. The horizontal axis represents the solution number in the Pareto solution set, and the vertical axis represents the comprehensive evaluation value calculated by the entropy weight method. Optimal output result: n = 3197.0320 r / min; = 0.1856mm / z; = 0.2503 mm; = 10.0000 mm; SEC = 12.844336; = 0.865692; w 1 = 0.1316, w 2 = 0.8684.
[0084] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.
Claims
1. A multi-objective cutting parameter optimization method, characterized in that, The method comprises the following steps: Step 100: collecting cutting parameters of selected workpiece materials and spindle power signals in the cutting process, calculating specific cutting energy, and collecting surface roughness of the workpiece surface at the same time; Step 200: constructing a BP neural network model, optimizing the weights and thresholds of the BP neural network by using the Harris hawk optimization algorithm, and establishing a specific cutting energy prediction model with cutting parameters as input and specific cutting energy as output by taking minimization of the fitness function as the optimization objective; Step 300: constructing a surface roughness prediction model with the coded variables of the cutting parameters as input and the surface roughness as output; Step 400: based on the specific cutting energy prediction model and the surface roughness prediction model, a multi-objective cutting parameter optimization model is established; Step 500: the multi-objective cutting parameter optimization model is solved to obtain a Pareto non-dominated solution set; Step 600: after obtaining the Pareto non-dominated solution set, an entropy weight method is used for comprehensive decision-making, and the solution with the maximum comprehensive evaluation value is selected as the optimal cutting parameter combination.
2. The method of claim 1, wherein, In step 100, the cutting parameters include the extreme values of the rotational speed, the feed per tooth, the axial cutting depth and the radial cutting depth.
3. The multi-objective cutting parameter optimization method according to claim 1 or 2, characterized in that, In step 100, the cutting parameters of the selected workpiece materials and the spindle power signals in the cutting process are collected, and the specific cutting energy is calculated, including: Based on the cutting parameters of the selected workpiece materials, the workpiece material removal rate is calculated; Based on the spindle power signal, the total energy consumed in the machining process is calculated by integration; Based on the workpiece material removal rate and the total energy consumed in the machining process, the specific cutting energy is calculated.
4. The method of claim 3, wherein, In step 100, it also includes: The collected cutting parameters and specific cutting energy are matched, and the collected cutting parameters and surface roughness are matched to construct an experimental data set; The experimental data set is preprocessed by normalization, and the preprocessed experimental data is divided into a training set and a test set.
5. The method of claim 4, wherein, In step 200, it includes: A BP neural network model is constructed, and the input layer is set as the cutting parameters and the output layer is set as the specific cutting energy; All connection weights and thresholds in the BP neural network model are coded as the position vectors of individuals in the Harris hawk optimization algorithm, and a fitness function is defined; The connection weights and thresholds of the BP neural network model are optimized by the Harris hawk optimization algorithm to minimize the fitness function, and a target function for nonlinear mapping between the cutting parameters and the specific cutting energy is established.
6. The method of claim 5, wherein, The fitness function is the sum of the mean square errors of the BP neural network model on the training set and the test set.
7. The method of claim 1, wherein, Step 300 includes: The cutting parameters are converted into coded variables; Based on the coded variables of the cutting parameters, a quadratic polynomial model is established by using the response surface method to represent the relationship between the coded variables of the cutting parameters and the surface roughness prediction value, i.e., the surface roughness prediction model.
8. The method of claim 1, wherein, In step 400, when establishing the multi-objective cutting parameter optimization model, the constraint conditions of the cutting parameters are also set.
9. The method of claim 1, wherein, In step 500, the multi-objective cutting parameter optimization model is solved by using the decomposition evolutionary algorithm to obtain a Pareto non-dominated solution set.
10. The method of claim 1, wherein, Step 600 includes: Based on the Pareto non-dominated solution set, each solution is processed by dimensionless treatment; Calculate the information entropy, and use the information entropy to calculate the weight of each objective function; The comprehensive evaluation value is calculated based on the solutions under each objective function after dimensionless processing and the weight of each objective function. Compare the comprehensive evaluation values of all solutions, and select the solution with the largest comprehensive evaluation value as the optimal combination of cutting parameters.